Finite Group Databasebeta

← #27194404

Subgroups — #27194404

Order 13184.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268456C211yesmaximal, characteristic
2#20268073C211yesmaximal, characteristic, complemented
3#20267993C211yesmaximal, characteristic
4#20267537C211yesmaximal, characteristic, complemented
5#20267523C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic
7#498×C103C211yesmaximal, characteristic, complemented
8C2×Q8×D103—21no—
9C2×#13110092—21no—
10#15693020—21no—
11#15692999—22no—
12#15692997—21no—
13C4×Dic206C2211yescharacteristic
14C4×D412C2211yescharacteristic
15#15692983—21no—
16#15692952—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692945—21no—
20#15692944—21no—
21C4⋊Q8×C103C2211yescharacteristic
22C4⋊Q8×C103C2211yescharacteristic
23#106×C103—22no—
24C4×C8×C103C2211yescharacteristic
25C2×Dic206—22no—
26C2×Dic206D411yescharacteristic
27Q8×D103—42no—
28Q8×D103—42no—
29C2×D412D411yescharacteristic
30C2×C4×D103—22no—
31C2×C4×D103—21no—
32#13110092—42no—
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C4⋊Dic103D411yescharacteristic
36C4⋊Dic103D411yescharacteristic
37Dic103⋊C4—22no—
38Dic103⋊C4—21no—
39(C2×D103)⋊C4—22no—
40(C2×D103)⋊C4—21no—
41C4×Dic103—21no—
42C2×Q8×C103—21no—
43C2×Q8×C103—21no—
44C2×C8×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103—21no—
47C4⋊C4×C103—21no—
48C4⋊C4×C103D412yes—
49C42×C103C2311yescharacteristic
50C22×D103—21no—
51Q8×C103—41no—
52Q8×C103—41no—
53Q8×C103—41no—
54Q8×C103—41no—
55C2×C4×C103—22no—
56C2×C4×C103—41no—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×Dic103—21no—
61C2×Dic103—21no—
62C2×Dic103—21no—
63D412—21no—
64D412SD1612yes—
65C4×D103—44no—
66C4×D103—41no—
67C4×D103—41no—
68Dic206—21no—
69Dic206—44no—
70Dic206SD1612yescomplemented
71C8×C103—22no—
72C103⋊C8—41no—
73C103⋊C8—41no—
74C22×C103#12011yescharacteristic
75C2×D103—22no—
76C2×D103—41no—
77C2×D103—41no—
78C4×C103—21no—
79C4×C103—42no—
80C4×C103—81no—
81C4×C103C2×SD1611yescharacteristic
82C4×C103C2×SD1611yescharacteristic
83C4×C103AGL(1,ℤ/8)11yescharacteristic
84C4×C103#13711yescharacteristic
85Dic103—22no—
86Dic103—41no—
87Dic103—41no—
88C2×C103#44811yescharacteristic
89C2×C103#45011yescharacteristic
90C2×C103#45611yescharacteristic
91D103—42no—
92#1651—1031nomaximal, Sylow
93C103#165111yescharacteristic, complemented, Sylow
94D4×Q8—1031no—
95#498D10311yescharacteristic, complemented
96#475—1031no—
97#461—1031no—
98#332—1031no—
99Q8⋊C8—1031no—
100D4⋊C8—1031no—
101C22×Q8—2061no—
102C2×SD16—2061no—
103C4⋊Q8—2061no—
104C4⋊Q8C2×D10311yescharacteristic
105C4⋊Q8C2×D10311yescharacteristic
106C22⋊Q8—2061no—
107C22⋊Q8—2062no—
108C4×Q8—1031no—
109C4×D4—1031no—
110C4×D4—2061no—
111#106—22no—
112#106—2061no—
113C4⋊C8—1031no—
114C4⋊C8—1031no—
115#103—2061no—
116#103—2061no—
117C4×C8C2×D10311yescharacteristic
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—1031no—
121C2×Q8—4122no—
122C2×Q8—4122no—
123C2×Q8—2062no—
124C2×D4—1031no—
125C22×C4—2062no—
126C22×C4—2061no—
127SD16—4122no—
128C2×C8—21no—
129C2×C8—2061no—
130C2×C8—2061no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—1031no—
135C4⋊C4—1031no—
136C4⋊C4—2062no—
137C4⋊C4—2061no—
138C4⋊C4C22⋊D10312yes—
139C22⋊C4—2062no—
140C22⋊C4—2061no—
141C42—2061no—
142C42C22×D10311yescharacteristic
143C23—2061no—
144Q8—41no—
145Q8—41no—
146Q8—41no—
147Q8—41no—
148Q8—1032no—
149Q8—4124no—
150Q8—2061no—
151D4—1032no—
152D4—2061no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—4124no—
156C2×C4—4121no—
157C2×C4—4121no—
158C2×C4—2061no—
159C2×C4—2061no—
160C2×C4—2061no—
161C2×C4D4×D10311yescharacteristic
162C2×C4D4×D10311yescharacteristic
163C2×C4C2×C22⋊D10311yescharacteristic
164C8—22no—
165C8—4121no—
166C8—4121no—
167C22—4121no—
168C22—4121no—
169C22—2062no—
170C22#1569298911yescharacteristic
171C4—21no—
172C4—42no—
173C4—81no—
174C4—4121no—
175C4—4121no—
176C4—2062no—
177C4SD16×D10311yescharacteristic
178C4SD16×D10311yescharacteristic
179C4#1569304811yescharacteristic
180C4#1569305011yescharacteristic
181C2—4122no—
182C2#2026792811yescharacteristic
183C2#2026794011yescharacteristic
184C2#2026797311yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#498×C103C2
socleC22×C103#120
prime radicalC2×D412D4
hypercenter#498D103
hypocenterC103#1651
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20268073C2semidirect
4. #20267537C2semidirect
5. #20267523C2semidirect
7. #498×C103C2semidirect
70. Dic206SD16semidirect
93. C103#1651semidirect
95. #498D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202684562
#202680732
#202679932
#202675372
#202675232
#202675202
#498×C1032
#1651103